Linear Transformations with Characteristic Subspaces That Are Not Hyperinvariant
نویسندگان
چکیده
If f is an endomorphism of a finite dimensional vector space over a field K then an invariant subspace X ⊆ V is called hyperinvariant (respectively, characteristic) if X is invariant under all endomorphisms (respectively, automorphisms) that commute with f . According to Shoda (Math. Zeit. 31, 611–624, 1930) only if |K| = 2 then there exist endomorphisms f with invariant subspaces that are characteristic but not hyperinvariant. In this paper we obtain a description of the set of all characteristic non-hyperinvariant subspaces for nilpotent maps f with exactly two unrepeated elementary divisors. Mathematics subject classification (2010): 15A18, 47A15, 15A57.
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